【摘要】 给出了有限域Fqn上多项式f(T)(x)是完全映射的充要条件是多项式f(x)和f(x)+1均与xn-1互素,其中T为有限域Fqn上一个固定的线性变换.利用有限域上的分圆多项式的有关结果,构造出次数较高而且项数比较多的一类完全映射.结果表明,这类完全映射在分组密码中S-盒的设计方面具有好的密码学性质.更多还原

【Abstract】 It is shown that the polynomial f（T）（x） is a complete mapping if and only if both f（x） and f（x）+1 are relatively prime to xⁿ+1,where T is a fixed linear transform on the finite field F_qⁿ.Furthermore,by using some results on cyclotomic polynomials some kinds of complete mappings with higher degrees and more terms are constructed.It is found that these complete mappings have good cryptographic properties for the S-boxes device in block cipher.更多还原